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Use Euclid\'s algorithms to find the HCF of 4052 and 12576

Answer»
According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r ≤ b.HCF is the largest number which exactly divides two or more positive integers.Since 12576 > 405212576 = (4052 × 3) + 420420 is a reminder which is not equal to zero (420 ≠ 0).4052 = (420 × 9) + 272271 is a reminder which is not equal to zero (272 ≠ 0).Now consider the new divisor 272 and the new remainder 148.272 = (148 × 1) + 124Now consider the new divisor 148 and the new remainder 124.148 = (124 × 1) + 24Now consider the new divisor 124 and the new remainder 24.124 = (24 × 5) + 4Now consider the new divisor 24 and the new remainder 4.24 = (4 × 6) + 0Reminder = 0Divisor = 4HCF of 12576 and 4052 = 4.

The HCF of 12576 and 4052 is 4


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